We prove the existence of a bounded positive solution for the following stationary Schrödinger equation
$ \begin{equation*} -\Delta u+V(x)u = f(x,u),\,\,\, x\in\mathbb{R}^n,\,\, n\geq 3, \end{equation*} $
where $ V $ is a vanishing potential and $ f $ has a sublinear growth at the origin (for example if $ f(x,u) $ is a concave function near the origen). For this purpose we use a Brezis-Kamin argument included in [
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